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Is the ordered pair (2, -1) a solution to the system 3x - y = 7 and x - 2y = 4?
AYes, it makes both equations true
BNo, it only makes the first equation true
CNo, it only makes the second equation true
DNo, it makes neither equation true
Answer & Solution
Correct answer: A. Yes, it makes both equations true
1. Substitute x = 2 and y = -1 into 3x - y = 7: 3(2) - (-1) equals 6 plus 1, which equals 7, a true statement.
2. Substitute the same values into x - 2y = 4: 2 - 2(-1) equals 2 plus 2, which equals 4, also a true statement.
3. Since the pair makes both equations true, it is a solution to the system.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.1 Solve Systems of Equations by Graphing_
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